As stated above, the weather will be a crapshoot in December.
February is also full of Europe's "half-term" school vacations.
Clears up 3rd week in February and that's when we usually go.
How long is your trip ?
The notion of staying a few days at a few places is a lot of travel / downtime.
I have skied St Anton, Garmish-Partenkirchen, and Zermatt ( Zermatt the last 2 years in a row ).
I have also had dialogue with poster "Cheizz" above ... heed his comments on the European ski scene.
My parents are both Austrian, so I love ALL of the European food & drink & schtik.
Garmisch is an interesting place as it is so close to Munich, and a fully functional town on its own, meaning lots of amenities and very little tourist gouging.
It has 2 ski areas, the "classic" and the glacier.
You are also very close drive to some Austrian ski areas for a ski day trip and back.
If you are bored, go back to Munich for a day and tour the old city & beer halls, and my obligatory stop at the BMW headquarters / museum.
Zermatt is at a high elevation and you can count on snow there almost year round.
It is a big ski area, connected to a smaller Italian ski area.
We spent 6 ski-days there no problem last year, and did not get bored, having already been there the year before.
The St. Anton scene is quite fun too, and lots of nearby ski areas.
Another ski friend and his group are very fond of the Val Gardena area, having been there 5-6 times now.
This year Ischgl is at the top of our list
Thanks Andy for a very in depth answer we will be going for about 10 days probably. With everyone saying that's a terrible time to go either in terms of no snow or too many people the only other time we may be able to go is end March I doubt that would be any better would it?